Chapter VII.
PROPERTIES OF GASES
The ideal gas model
- a first model to imagine how gases are
1. enormous number of tinny particles separated
by relatively large distances
2. particles are sphere-like, have no internal
structure and are indestructible
3. they do not interact with each other except
when they collide with each other and the
container's wall
4. between collision particles move in straight
line with considerably high speed
5. collision totally elastic one
- describes qualitatively well the macroscopic
behavior of not too dense gases
(variation of macroscopic properties in
different conditions)
- it is in accordance with direct observations
on the movement of molecules
Brownian motion  1827 Scottish botanist
Robert Brown
- erratic and continuos motion of pollen
particles mixed in water
- explained rigorously in 1905 by Einstein
Macroscopic parameters of the ideal gases
1. volume (V) (units in SI  1 m3)
2. mass (M)
3. pressure (P)  it is a result of the atomic motion
Pressure is the force exerted perpendicularly on
a surface divided by the area of the surface.
(Force per unit area)-scalar quantity !!!
F
; units in SI: 1 N/m2 , called Pa (Pascal)
A
- due to the continuos collision of molecules with the
wall of container the molecules act with a force on
the wall the wall experience the pressure of the gas
- shrinking the volume of the container more
frequent collision increase in the P
- increasing the number of particles more frequent
collision increase in P
- increasing the temperaturemovement of
molecules with bigger speed increase in P
4. temperature (T)
- usually defined asour feelings of hot and cold
- subjective feelings of hot and cold are not accurate
- accurately  assign numbers to temperatures
done by thermometers
P
-first thermometer  Galileo
-replaced by the alcohol-in-glass thermometer
-nowadays bimetals, semiconductor sensors,
thermocouples etc…
The main problem standardizing the scales !!!
(temperature values be reproducible)
we need two reproducible temperatures and divide
the interval between them in equal divisions
 first scale proposed by Newton (1701)
I. temperaturea mixture of ice + water
II. temperature human body temperature
interval divided in 12 equal divisions
 Gabriel Fahrenheit propose for the
II. temperaturebiling point of pure water
I. temp.=32 0 F; II. temp.=212 0 F
Fahrenheit temperature scale
 a new scale in 1948
I. temp.=0 0 C; II. temp.=100 0 C
Celsius temperature scale
 for SI a new scale defined by the properties
of ideal gases, distance between units is kept
I. temperature the lowest possible
temperature where the volume of ideal gases
would go to zero  0 0 K=-273 0 C
II. temperature where water freezes
273 0 K=0 0 C
Kelvin temperature scale or
absolute temperature scale
Microscopic parameters of ideal gases
1. mass of one molecule (m)
2. number of molecules (N)
3. speed of a given molecule (v)
- different molecules might have different speed
- the value of speed is changing in time
- experiment to study the speed distribution of
particles rotating drum experiment
Result:
- most of the particles have speed near
the average speed,
- average speed quite high value (500m/s)
- few particles with low and high speed
- speed increases as the temperature increases
(the mean velocity at the square is proportional
with the temperature): v ~ T
4. kinetic energy of molecules (Ek)
E  ~ T

5.momentum of molecules ( p )
2
k
The Ideal Gas Law
The three macroscopic properties of a given gas:
volume, temperature and pressure-are related by
a relationship known as the ideal gas law.
This law states: PV  cT
P the pressure; Vvolume; Tabsolute
thermodynamic temperature c a constant which
depends on the amount of gas
The ideal gas law is a combination of three
experimentally discovered relationships!
I.
For a given ideal gas held at constant
temperature the product of pressure and
volume is a constant
1
if T=const  PV=const P ~
V
II. For a given ideal gas held at constant volume
the pressure is linearly proportional with the
absolute thermodynamic temperature
if V=const P~T
III. For a given ideal gas at constant pressure the
volume is linearly proportional with the
absolute thermodynamic temperature
if P=constV~T
Home-work assignments:
181/24-28, 181/30-33, 181/37-42, 182/51-54
183/17-20, 183/23-24